The dynamics of cooperation, power, and inequality in a group-structured society

Most human societies are characterized by the presence of different identity groups which cooperate but also compete for resources and power. To deepen our understanding of the underlying social dynamics, we model a society subdivided into groups with constant sizes and dynamically changing powers. Both individuals within groups and groups themselves participate in collective actions. The groups are also engaged in political contests over power which determines how jointly produced resources are divided. Using analytical approximations and agent-based simulations, we show that the model exhibits rich behavior characterized by multiple stable equilibria and, under some conditions, non-equilibrium dynamics. We demonstrate that societies in which individuals act independently are more stable than those in which actions of individuals are completely synchronized. We show that mechanisms preventing politically powerful groups from bending the rules of competition in their favor play a key role in promoting between-group cooperation and reducing inequality between groups. We also show that small groups can be more successful in competition than large groups if the jointly-produced goods are rivalrous and the potential benefit of cooperation is relatively small. Otherwise large groups dominate. Overall our model contributes towards a better understanding of the causes of variation between societies in terms of the economic and political inequality within them.

Design and Optimal Control of a Multistable, Cooperative Microactuator

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty.

Modelling microbiome recovery after antibiotics using a stability landscape framework

Treatment with antibiotics is one of the most extreme perturbations to the human microbiome. Even standard courses of antibiotics dramatically reduce the microbiome’s diversity and can cause transitions to dysbiotic states. Conceptually, this is often described as a ‘stability landscape’: the microbiome sits in a landscape with multiple stable equilibria, and sufficiently strong perturbations can shift the microbiome from its normal equilibrium to another state. However, this picture is only qualitative and has not been incorporated in previous mathematical models of the effects of antibiotics. Here, we outline a simple quantitative model based on the stability landscape concept and demonstrate its success on real data. Our analytical impulse-response model has minimal assumptions with three parameters. We fit this model in a Bayesian framework to data from a previous study of the year-long effects of short courses of four common antibiotics on the gut and oral microbiomes, allowing us to compare parameters between antibiotics and microbiomes, and further validate our model using data from another study looking at the impact of a combination of last-resort antibiotics on the gut microbiome. Using Bayesian model selection we find support for a long-term transition to an alternative microbiome state after courses of certain antibiotics in both the gut and oral microbiomes. Quantitative stability landscape frameworks are an exciting avenue for future microbiome modelling.

A Note on Trial Delay and Social Welfare: The Impact of Multiple Equilibria

Greater trial delay is commonly associated with decreasing demand for trials, thereby bringing about an equilibrium for a given trial capacity. This note highlights that – in contrast to this premise – trial delay may in fact increase trial demand. Such an outcome is established for a scenario in which the number of cases is endogenous based on the deterrence effect of lawsuits. That trial demand may increase with longer delay makes multiple stable equilibria possible. This reality has important policy implications, which are discussed.

COEXISTENCE OF MULTISTABILITY AND CHAOS IN A RING OF DISCRETE NEURAL NETWORK WITH DELAYS

A ring of discrete-time delayed neural network with self-feedback and a valid nonmonotonic activation function is explored. Coexistence of multiple stable equilibria and chaotic dynamics are demonstrated in this discrete dynamical system. Specifically, 2m stable stationary solutions and their basins of attraction are found for a loop with m-neurons network. The theory is established by formulating parameter conditions according to a geometric observation. The networks are further confirmed to exhibit chaotic dynamics when the magnitudes of inhibitory self-feedback weights are large enough. The scenario is based on building a snapback repeller and Marotto's theorem.

STABILITY, SYMMETRY-BREAKING BIFURCATIONS AND CHAOS IN DISCRETE DELAYED MODELS

In this paper, we use the standard bifurcation theory to study rich dynamics of time-delayed coupling discrete oscillators. Equivariant bifurcations including equivariant Neimark–Sacker bifurcation, equivariant pitchfork bifurcation and equivariant periodic doubling bifurcation are analyzed in detail. In the application, we consider a ring of identical discrete delayed Ikeda oscillators. Multiple oscillation patterns, such as multiple stable equilibria, stable limit cycles, stable invariant tori and multiple chaotic attractors, are shown.

EXOGENOUS REINFECTION AND RESURGENCE OF TUBERCULOSIS: A THEORETICAL FRAMEWORK

The importance of exogenous reinfection versus endogenous reactivation for the resurgence of tuberculosis (TB) has been a matter of ongoing debate. Previous mathematical models of TB give conflicting results on the possibility of multiple stable equilibria in the presence of reinfection, and hence the failure to control the disease even when the basic reproductive number is less than unity. The present study reconsiders the effect of exogenous reinfection, by extending previous studies to incorporate a generalized rate of reinfection as a function of the number of actively infected individuals. A mathematical model is developed to include all possible routes to the development of active TB (progressive primary infection, endogenous reactivation, and exogenous reinfection). The model is qualitatively analyzed to show the existence of multiple equilibria under realistic assumptions and plausible range of parameter values. Two examples, of unbounded and saturated incidence rates of reinfection, are given, and simulation results using estimated parameter values are presented. The results reflect exogenous reinfection as a major cause of TB emergence, especially in high prevalence areas, with important public health implications for controlling its spread.

Dynamic Response of Dielectric Elastomers

Dielectric elastomers have received a great deal of attention recently for effectively transforming electrical energy to mechanical work. Their large strains and conformability make them enticing materials for many new types of actuators. Unfortunately, their non-linear material behavior and large deformations make actual devices difficult to model. However, the reason for this difficulty can also be used to design actuators that utilize these material and geometric non-linearities to obtain multiple stable equilibria. In this work, we investigate one of the simplest possible configurations, a spherical membrane, using a model that incorporates both mechanical and electrostatic pressure as well as inertial effects that become important when transitioning from one equilibrium to another.